APPROXIMATE ANGULAR MOMENTUM PROJECTION OF THE DEFORMED HARTREE-FOCK STATE FOR K=1

Using our approximate angular momentum projection method with one parameter, the projection spectra of the axially symmetric Hartree-Fock intrinsic states are studied. The approximate and the exact projection matrix elements are obtained and compared each other. The projection integrals for angular momentum J=1 to 11 are given. The energy spectra of the nuclei ⁴⁴Ti and ⁵⁰Ti are calculated, and the results coincide with the observed energy levels fairly well.     

Microscopical Studies of the Energy Staggering in γ-Soft Nuclei

The energy staggering in γ-or quasi γ-band of γ-soft even-even nuclei is studied with the approximate angular moment um projection of the deformed Hartree-Fock (DHF) states. In the calculations of DHF states the modified surface &interaction matrix elements are used. It is found that in the K = 2 band produced by the angular momentum projection of DHF state the energy staggering appears only in certain conditions. Some points concerning with the angular momentum projection of K = 2 DHF states are discussed. The energy spectra of nuclei ⁷⁴Se and ⁷⁶Kr are calculated and compared with the experimental data, which show the staggering pattern of γ-soft rotor, the coincidence between them are fairly good.     

On number and angular momentum projection from Hartree-Bogoliubov states

Rotational spectra, calculated by angular momentum projection from Hartree-Bogoliubov states may be completely distorted by particle number nonconservation. A simple method for correcting this is presented, which brings them close to the number projected spectra. It is also shown that by a slight modification of the usual number projection operator this projection may then be executed two times faster and with better numerical accuracy. We study the effect ofJ- and/orN projection before the variation in a constrained Hartree-Bogoliubov model. It is demonstrated that only simultaneous projection of both particle number and angular momentum before the variation is meaningful. Then a more gradual antipairing effect is found than known from previous work. We conclude however that the diagonalization of the Hamiltonian in a space of appropriately chosen generator wave functions is preferable to projection before the variation. In all cases the examples are nuclei in thesd-shell, calculated selfconsistently without separating off and inert core. The nucleon-nucleon force is the Hamada-Johnston potential.     

Angular-momentum-projected cranked hfb approach to the study of nuclear rotations

Employing a pairing-plus-quadrupole interaction hamiltonian and projecting out good angular momentum states from the cranked Hartree-Fock-Bogoliubov (CHFB) intrinsic wave functions the yrast spectra of ¹⁵⁸Dy and ¹⁶⁸Yb are calculated up to moderately high spins (I_max = 16) as to include the backbending region. Then the variation of pairing correlation, g-factor and rotational alignment of neutron spin as a function of total angular momentum is studied. The effect of particle number projection on the spin-projected CHFB wave functions is also investigated and is found to be unimportant for the calculation of g-factors. On the other hand, corrections of the excitation energies for number fluctuations in the CHFB wave functions are essential. Furthermore, looking at the distribution of the total projection quantum number K in various cranking wave functions we are able to throw some light on the K ≠ 0 nature of the aligned s-band.A variation-after-spin projection calculation strictly for the axial shape, without cranking, is also carried out for both the nuclei considered here. In the low-spin region this numerically “cheaper” scheme produces energy spectra similar to that of the CHFB method, and may thus be used to readjust the interaction parameters.     

推转PNC波函数的角动量投影

研究原子核较高自旋态的特征,不仅需要考虑K混合,而且应该引入Coriolis相互作用项,亦即使用推转Hamilton量.推转项的引入破坏了时间反演对称性,单粒子角动量在内禀对称轴上的投影量子数已不再是好量子数.从表面上看,这会使得理论计算变得非常复杂,但考虑到原子核的某些固有对称性,将角动量投影技术应用于含推转成份的粒子数守恒波函数(推转PNC波函数)并不十分困难.在这一理论框架下详细推导计算原子核能谱及电磁性质的基本表达式,从而表明实施该方案的可行性.     

The angular momentum dependence of correlations in the ground state rotational spectra of20Ne and22Ne

Multi-Configuration-Hartree-Fock (MCHF) calculations with angular momentum projection before the variation of the internal degrees of freedom have been performed for the nuclei²⁰Ne and²²Ne. This procedure yields different correlated intrinsic states for the different members of a rotational band. Thus the angular momentum dependence of correlations has been studied. Experimentally, the ground state spectra of²⁰Ne and²²Ne show properties similar to the phase transitions observed in some rare earth nuclei which have been well reproduced through the present calculations. The calculated spectra andBE2-values show a significant improvement compared to the ones obtained by variation before the angular momentum projection is effected.     

The projected Hartree-Fock spectra from a realistic two-body interaction

The projection method is used to obtain good angular momentum and good isospin states from the intrinsic Hartree-Fock states of the nuclei in the 2s-1d shell. An effective interaction derived from the Yale potential has been employed in the calculations. It is found that the static magnetic moments are predicted correctly. The static quadrupole moments and the lifetimes of the nuclear states for electric quadrupole transitions are predicted correctly if an effective charge of 0.5 e is ascribed to the neutrons. The projected energy spectra in even-mass nuclei are very much compressed as compared to the experimental spectra. The agreement between the projected and the experimental spectra in odd-mass nuclei is not so bad.     

量子点电子态的尺寸效应和磁场的影响

在有效质量近似下，使用少体物理的方法，计算了在不同大小约束势情况下二维量子点三电子系统的自旋极化态的能谱.结果显示幻数角动量是否出现，主要取决于量子力学对称性、约束势大小及磁场的强度. 关键词：     

A description of decoupled bands using the angular momentum projection method applied to the coherent phonon state

The decoupled bands of the odd-A La-isotopes are described by the angular momentum projection method. The coherent phonon state is assumed for the intrinsic wave function of the core. The present model covers the particle-vibrator and the particle-rotor coupling model. The results are in good agreement with the experimental energy spectra.     

Energy Staggering in the High K Rotational Band

Introducing the staggering index S(I) to describe the energy spectra of the λrigid and λ-soft nuclei, it becomes very clear that there are two kinds of energy staggering for which the S(I) -I plots have opposite zigzag behavior. They can be described using the axially asymmebtric rotor model with vibration-rotation coupling and the interaction boson model O(6) limit with three-body potential or the angular momentum projection deformed Hartree-Fock method (PDHF ), respectively. The theoretical predictions for the characteristics of the staggering in high K rotational band are given. Analyzing the experimental data of high K band spectra of the nuclei in the mass range. 160, it is demoastrated that the energy staggering does exist in the high K band. At the same time, some evidences for the shape transition indicated by zigzag phase change of S(I)-I plots are undoubtedly found.     

Nuclear Level Density with Non-zero Angular Momentum

The statistical properties of interacting fermions have been studied for various angular momentum with the inclusion of pairing interaction. The dependence of the critical temperature on angular momentum for several nuclei,have been studied. The yrast energy as a function of angular momentum for 28 Si and 24Mg nuclei have been calculated up to 60.0 MeV of excitation energy. The computed limiting angular momenta are compared with the experimental results for 26Al produced by 12C 14N reaction. The relevant nuclear level densities for non-zero angular momentum have been computed for 44Ti and l36Ba nuclei. The results are compared with their corresponding values obtained from the approximateformulas.     

An approximate projection technique for the calculation of electromagnetic properties of deformed nuclei

A three-dimensional angular momentum projection is carried out for cranking model wave functions. The projected matrix elements of electromagnetic operators are evaluated using a method originally developed by Kamlah for the case of projected energy, which is valid for large deformations and weakly triaxial nuclei. The calculated spectroscopic quadrupole moments deviate substantially from the predictions of a rigid rotor model with axial symmetry. For E2 transitions the deviations are small. Projected values of the magnetic moments are almost identical with those of a semiclassical calculation. Cranking model wave functions are decomposed into its components having good angular momentum.     

偶偶Ge和Se同位素核的形变HF态及负宇称带研究

将具有负宇称的fp轨道空间扩大到包含具有正宇称的1g_9/2轨道,采用修正的表面δ相互作用,对⁶⁴Ge,⁶⁶Ge,⁶⁸Ge,⁷⁰Se,⁷²Se和⁷⁴Se等6个偶偶核做了形变HF计算.得到了基态和一些激发态的解.同时,还用近似角动量投影形变Hartree-Fock(PDHF)方法,对⁶⁴Ge和⁷⁴Se进行了能谱计算,得到其正、负宇称带的解,计算结果与实验谱基本一致.     

偶偶Cd同位素核的形变HF态及负宇称带研究

将具有正宇称的轨道空间扩大到包含具有负宇称的1h_11/2轨道,采用修正的表面δ相互作用(MSDI),对¹⁰⁴Cd,¹⁰⁶Cd,¹⁰⁸Cd,¹¹⁰Cd,¹¹²Cd,¹¹⁴Cd和¹¹⁶Cd等7个偶偶核作了形变HF计算.得到了基态和一些激发态的解.同时,还用近似角动量投影形变Hartree-Fock(PDHF)方法对¹⁰⁸Cd和¹¹⁰Cd进行了能谱计算,得到其正、负宇称带的解,计算结果与实验谱基本一致.     

190，192Pb原子核的超形变带的带外衰变（英文）

将基于组合方法的角动量投影的位能曲面群用于研究铅同位素原子核190,192Pb 的超形变转动带。位能曲面群计算中采用了Gogny D1S 以及Skyrme SkP SLy4 三种相互作用。如用Gogny D1S 相互作用,190Pb 原子核没有明显的超形变转动带,而192Pb 原子核有非常显著的超形变转动带。用W. K. B. 方法计算了192Pb 原子核的超形变带穿透宽度。该穿透宽度很大与用GW模型（Nucl. Phys. A 660 （1999）197）分析实验数据给出的结果相近。在Gogny D1S 相互作用情形下,就角动量投影对位能曲面群的影响作了讨论,发现角动量投影压低了分隔超形变转动带与正常形变转动带之间的位垒。还用Skyrme SkP 和SLy4 相互作用计算了角动量投影的位能曲面群,发现位垒明显高于Gogny D1S 相互作用给出的位垒。在Skyrme 相互作用情形下,192Pb 原子核的超形变带穿透宽度明显小于Gogny 相互作用给出的宽度,但是较SB方法（Phys. Rev. C,60 （1999） 051305） 分析实验数据得到的结果高出几个数量级。于是,对SB 方法提出了质疑,因为它给出了极其微小的传播宽度。The combined method is applied to calculate the angular momentum projected potential energy surfaces (AMPPES) of 190,192Pb. The Supper-deformed(SD) rotational bands of the two nuclei are studied with the AMPPES computed with the Gogny D1S and Skyrme SkP and SLy4 interactions. It is found that there is no pronounced SD band in 190Pb in the case of the Gogny interaction, which is consistent with the experimental observation. A well developed SD band with the Gogny interaction is found in 192Pb. The tunneling width of 192Pb is comparable to that given by the GW approach (Nucl. Phys. A 660 (1999)197) and orders of magnitude larger than that given by the SB approach (Phys. Rev. C 60 (1999) 051305). The influence of the angular momentum projection on the potential energy surfaces is examined in the case of the Gogny interaction for 190,192Pb. It is shown that the angular momentum projection suppresses the barrier separating the SD and ND rotational bands. Higher barriers of the AMPPESs for the two nuclei computed with the Skyrme SkP and SLy4 interactions are obtained compared with those given by the Gogny force. The tunneling width of 192Pb is also big for the Skyrme interactions. We put the SB approach into question which gives only an extremely small spreading width.     

Nuclear Level Density with Non-zero Angular Momentum

The statistical properties of interacting fermions have been studied for various angular momentum with the inclusion of pairing interaction. The dependence of the critical temperature on angular momentum for several nuclei, have been studied. The yrast energy as a function of angular momentum for 28Si and 24 Mg nuclei have been calculated up to 60.0 MeV of excitation energy. The computed limiting angular momenta are compared with the experimental results for ^26Al produced by ^12C＋ 14N reaction. The relevant nuclear level densities for non-zero angular momentum have been computed for ^44Ti and ^136 Ba nuclei. The results are compared with their corresponding values obtained from the approximate formulas.     

Cold nuclear matter effects on dijet productions in relativistic heavy-ion reactions at LHC

We investigate the cold nuclear matter (CNM) effects on dijet productions in high-energy nuclear collisions at LHC with the next-to-leading order perturbative QCD. The nuclear modifications for dijet angular distributions, dijet invariant mass spectra, dijet transverse momentum spectra and dijet momentum imbalance due to CNM effects are calculated by incorporating EPS, EKS, HKN and DS parametrization sets of parton distributions in nucleus. It is found that dijet angular distributions and dijet momentum imbalance are insensitive to the initial-state CNM effects and thus provide optimal tools to study the final-state hot QGP effects such as jet quenching. On the other hand, the invariant mass spectra and the transverse momentum spectra of dijet are generally enhanced in a wide region of the invariant mass or transverse momentum due to CNM effects with a feature opposite to the expected suppression because of the final-state parton energy loss effect in the QGP. The difference of EPS, EKS, HKN and DS parametrization sets of nuclear parton distribution functions is appreciable for dijet invariant mass spectra and transverse momentum spectra at p+Pb collisions, and becomes more pronounced for those at Pb+Pb reactions.     

Two-dimensional photoelectron momentum distribution of hydrogen in intense laser field

Two-dimensional (2D) electron momentum distributions and energy spectra of a hydrogen in an intense laser field are calculated by solving the time-dependent Schrödinger equation combined with the window-operator technique. Compared with the standard projection technique, the window-operator technique has the advantage that the continuum states of atoms can be avoided in the calculation. We show that the 2D electron momentum distributions and the energy spectra from those two techniques accord quite well with each other if an appropriate energy width is used in the window operator.     

20MeV到180MeV／u~（16）O＋~（197）Au系统的BUU计算：线动量与角动量转移依赖碰撞参数与能量研究

用考虑了角动量守恒的ＢＵＵ模型计算了２０ＭｅＶ≤Ｅ／ｕ≤１８０ＭｅＶ能区１６Ｏ＋１９７Ａｕ系统的反应线性动量转移（ＬＭＴ）及余核角动量，着重讨论了反应线性动量转移及余核角动量对反应碰撞参量、入射能Ｅ／ｕ的依赖关系，比较了计算ＬＭＴ与Ｖｉｏｌａ系统性给出的结果间的偏差．计算结果揭示了当Ｅ／ｕ≥９０ＭｅＶ时，余核角动量对Ｅ／ｕ增长出现的饱和现象，主要来源于靶核对弹核捕获能力的持续丢失．     

Nuclear absorption of stopped antiprotons: Multipion-nucleus interactions

It is proposed to use the nuclear absorption of stopped antiprotons to study the interaction arising when several pions enter a nucleus simultaneously. A model is constructed for the incoherent multipion-nucleus interaction, when the annihilation pions interact with the nucleus independently of each other. Energy spectra and the multiplicities of secondary particles generated after the antiproton absorption are compared with the experimental data. Distributions of the number of pions interacting with the nucleus are calculated as well as the distributions of residual nuclei with excitation energy, momentum, angular momentum and isotope yield. It is shown that the effect of the excitation of high-spin isomers must be observed in the antiproton absorption. The example of the two-nucleon absorption of η- and ω-mesons is used to discuss the possibility of investigating interactions of pionic resonances with nuclei during the process of the annihilation of antiprotons.